81 citations · 403 across the 47 of their papers we have counts for
7 papers · 1 filter
Enumerating fundamental normal surfaces: Algorithms, experiments and invariants
Benjamin A. Burton
Computational knot theory and 3-manifold topology have seen significant breakthroughs in recent years, despite the fact that many key algorithms have complexity bounds that are exp…
Simplification paths in the Pachner graphs of closed orientable 3-manifold triangulations
Benjamin A. Burton
It is important to have effective methods for simplifying 3-manifold triangulations without losing any topological information. In theory this is difficult: we might need to make a…
Triangulating a Cappell-Shaneson knot complement
Ryan Budney, Benjamin A. Burton, Jonathan Hillman
We show that one of the Cappell-Shaneson knot complements admits an extraordinarily small triangulation, containing only two 4-dimensional simplices.
Computing the crosscap number of a knot using integer programming and normal surfaces
Benjamin A. Burton, Melih Ozlen
The crosscap number of a knot is an invariant describing the non-orientable surface of smallest genus that the knot bounds. Unlike knot genus (its orientable counterpart), crosscap…
Multi-objective integer programming: An improved recursive algorithm
Melih Ozlen, Benjamin A. Burton, Cameron A. G. MacRae
This paper introduces an improved recursive algorithm to generate the set of all nondominated objective vectors for the Multi-Objective Integer Programming (MOIP) problem. We signi…
Locating regions in a sequence under density constraints
Benjamin A. Burton, Mathias Hiron
Several biological problems require the identification of regions in a sequence where some feature occurs within a target density range: examples including the location of GC-rich…